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Simulating resource movements and markets: A continuous dynamical system with delays to model anthropogenic metal cycles

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  • Gambaro, Nicola
  • Brito-Parada, Pablo
  • Glöser-Chahoud, Simon
  • Plancherel, Yves

Abstract

A material flow analysis and mineral commodity model based on ordinary and delay differential equations is derived from first principles in physics and economics, namely conservation of mass and the cobweb theorem. The dynamical system models anthropogenic metal stocks, flows and markets, including prices. An application to copper is demonstrated. Numerical simulations show that the model is able to reproduce the dynamics of the anthropogenic stocks and flows as well as the broad, long-term trends or cycles in the market variables. In the model, longer mining lead times generate more volatile and more prolonged market cycles, while shorter ones have the opposite effect. The present approach is capable of quantitatively representing the relationship between material and price movements by considering the resource cycle as a system that is both physical and socio-economic in nature.

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  • Gambaro, Nicola & Brito-Parada, Pablo & Glöser-Chahoud, Simon & Plancherel, Yves, 2025. "Simulating resource movements and markets: A continuous dynamical system with delays to model anthropogenic metal cycles," Resources Policy, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:jrpoli:v:103:y:2025:i:c:s030142072500090x
    DOI: 10.1016/j.resourpol.2025.105548
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    1. Dewulf, Jo & Blengini, Gian Andrea & Pennington, David & Nuss, Philip & Nassar, Nedal T., 2016. "Criticality on the international scene: Quo vadis?," Resources Policy, Elsevier, vol. 50(C), pages 169-176.
    2. Simon Glöser-Chahoud & Johannes Hartwig & I. David Wheat & Martin Faulstich, 2016. "The cobweb theorem and delays in adjusting supply in metals' markets," System Dynamics Review, System Dynamics Society, vol. 32(3-4), pages 279-308, July.
    3. Humphreys, David, 2010. "The great metals boom: A retrospective," Resources Policy, Elsevier, vol. 35(1), pages 1-13, March.
    4. John E. Tilton, 2018. "Assessing the market power of mineral commodity producers," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 31(1), pages 71-76, May.
    5. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
    6. Yan, Lingyu & Wang, Anjian & Chen, Qishen & Li, Jianwu, 2013. "Dynamic material flow analysis of zinc resources in China," Resources, Conservation & Recycling, Elsevier, vol. 75(C), pages 23-31.
    7. T. E. Graedel & Dick van Beers & Marlen Bertram & Kensuke Fuse & Robert B. Gordon & Alexander Gritsinin & Ermelinda M. Harper & Amit Kapur & Robert J. Klee & Reid Lifset & Laiq Memon & Sabrina Spatari, 2005. "The Multilevel Cycle of Anthropogenic Zinc," Journal of Industrial Ecology, Yale University, vol. 9(3), pages 67-90, July.
    8. van der Voet, Ester & Kleijn, Rene & Huele, Ruben & Ishikawa, Masanobu & Verkuijlen, Evert, 2002. "Predicting future emissions based on characteristics of stocks," Ecological Economics, Elsevier, vol. 41(2), pages 223-234, May.
    9. Stuermer, Martin, 2017. "Industrialization and the demand for mineral commodities," Journal of International Money and Finance, Elsevier, vol. 76(C), pages 16-27.
    10. Colin A. Carter & Gordon C. Rausser & Aaron Smith, 2011. "Commodity Booms and Busts," Annual Review of Resource Economics, Annual Reviews, vol. 3(1), pages 87-118, October.
    11. Nicholas Kaldor, 1934. "A Classificatory Note on the Determinateness of Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 1(2), pages 122-136.
    12. Franklin M. Fisher & Paul H. Cootner & Martin N. Baily, 1972. "An Econometric Model of the World Copper Industry," Bell Journal of Economics, The RAND Corporation, vol. 3(2), pages 568-609, Autumn.
    13. Radetzki, Marian, 2006. "The anatomy of three commodity booms," Resources Policy, Elsevier, vol. 31(1), pages 56-64, March.
    14. Gang Liu & Colton E. Bangs & Daniel B. Müller, 2013. "Stock dynamics and emission pathways of the global aluminium cycle," Nature Climate Change, Nature, vol. 3(4), pages 338-342, April.
    15. C. A. Tapia Cortez & J. Coulton & C. Sammut & S. Saydam, 2018. "Determining the chaotic behaviour of copper prices in the long-term using annual price data," Palgrave Communications, Palgrave Macmillan, vol. 4(1), pages 1-13, December.
    16. Rosenau-Tornow, Dirk & Buchholz, Peter & Riemann, Axel & Wagner, Markus, 2009. "Assessing the long-term supply risks for mineral raw materials--a combined evaluation of past and future trends," Resources Policy, Elsevier, vol. 34(4), pages 161-175, December.
    17. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    18. Junyang Wang & Kolyan Ray & Pablo Brito‐Parada & Yves Plancherel & Tom Bide & Joseph Mankelow & John Morley & Julia A. Stegemann & Rupert Myers, 2024. "Bayesian material flow analysis for systems with multiple levels of disaggregation and high dimensional data," Journal of Industrial Ecology, Yale University, vol. 28(6), pages 1409-1421, December.
    19. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    20. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
    21. Warburton, R.D.H. & Disney, S.M., 2007. "Order and inventory variance amplification: The equivalence of discrete and continuous time analyses," International Journal of Production Economics, Elsevier, vol. 110(1-2), pages 128-137, October.
    22. Hatayama, Hiroki & Daigo, Ichiro & Matsuno, Yasunari & Adachi, Yoshihiro, 2012. "Evolution of aluminum recycling initiated by the introduction of next-generation vehicles and scrap sorting technology," Resources, Conservation & Recycling, Elsevier, vol. 66(C), pages 8-14.
    23. Saleem H. Ali & Damien Giurco & Nicholas Arndt & Edmund Nickless & Graham Brown & Alecos Demetriades & Ray Durrheim & Maria Amélia Enriquez & Judith Kinnaird & Anna Littleboy & Lawrence D. Meinert & R, 2017. "Correction: Corrigendum: Mineral supply for sustainable development requires resource governance," Nature, Nature, vol. 547(7662), pages 246-246, July.
    24. Saleem H. Ali & Damien Giurco & Nicholas Arndt & Edmund Nickless & Graham Brown & Alecos Demetriades & Ray Durrheim & Maria Amélia Enriquez & Judith Kinnaird & Anna Littleboy & Lawrence D. Meinert & R, 2017. "Mineral supply for sustainable development requires resource governance," Nature, Nature, vol. 543(7645), pages 367-372, March.
    25. Soetaert, Karline & Petzoldt, Thomas & Setzer, R. Woodrow, 2010. "Solving Differential Equations in R: Package deSolve," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i09).
    26. Brian J. Henderson & Neil D. Pearson & Li Wang, 2015. "Editor's Choice New Evidence on the Financialization of Commodity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1285-1311.
    27. Elshkaki, Ayman & van der Voet, Ester & Timmermans, Veerle & Van Holderbeke, Mirja, 2005. "Dynamic stock modelling: A method for the identification and estimation of future waste streams and emissions based on past production and product stock characteristics," Energy, Elsevier, vol. 30(8), pages 1353-1363.
    28. Park, Jeong-a & Hong, Seok-jin & Kim, Ik & Lee, Ji-yong & Hur, Tak, 2011. "Dynamic material flow analysis of steel resources in Korea," Resources, Conservation & Recycling, Elsevier, vol. 55(4), pages 456-462.
    29. Gomez, Fernando & Guzman, Juan Ignacio & Tilton, John E., 2007. "Copper recycling and scrap availability," Resources Policy, Elsevier, vol. 32(4), pages 183-190, December.
    30. Yupeng Liu & Jiajia Li & Wei‐Qiang Chen & Lulu Song & Shaoqing Dai, 2022. "Quantifying urban mass gain and loss by a GIS‐based material stocks and flows analysis," Journal of Industrial Ecology, Yale University, vol. 26(3), pages 1051-1060, June.
    31. Kapur, Amit, 2006. "The future of the red metal—A developing country perspective from India," Resources, Conservation & Recycling, Elsevier, vol. 47(2), pages 160-182.
    32. Radetzki, Marian & Eggert, Roderick G. & Lagos, Gustavo & Lima, Marcos & Tilton, John E., 2008. "The boom in mineral markets: How long might it last?," Resources Policy, Elsevier, vol. 33(3), pages 125-128, September.
    33. Tapia, Carlos & Coulton, Jeff & Saydam, Serkan, 2020. "Using entropy to assess dynamic behaviour of long-term copper price," Resources Policy, Elsevier, vol. 66(C).
    34. Blomberg, Jerry & Söderholm, Patrik, 2009. "The economics of secondary aluminium supply: An econometric analysis based on European data," Resources, Conservation & Recycling, Elsevier, vol. 53(8), pages 455-463.
    35. Tilton, John E. & Humphreys, David & Radetzki, Marian, 2011. "Investor demand and spot commodity prices," Resources Policy, Elsevier, vol. 36(3), pages 187-195, September.
    36. Tcha, M. & Takashina, G., 2002. "Is world metal consumption in disarray?," Resources Policy, Elsevier, vol. 28(1-2), pages 61-74.
    37. Mastroeni, Loretta & Vellucci, Pierluigi & Naldi, Maurizio, 2018. "Co-existence of stochastic and chaotic behaviour in the copper price time series," Resources Policy, Elsevier, vol. 58(C), pages 295-302.
    38. Gleich, Benedikt & Achzet, Benjamin & Mayer, Herbert & Rathgeber, Andreas, 2013. "An empirical approach to determine specific weights of driving factors for the price of commodities—A contribution to the measurement of the economic scarcity of minerals and metals," Resources Policy, Elsevier, vol. 38(3), pages 350-362.
    39. Slade, Margaret E., 1980. "An econometric model of the U.S. secondary copper industry: Recycling versus disposal," Journal of Environmental Economics and Management, Elsevier, vol. 7(2), pages 123-141, June.
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